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Let $R\ $be an integral domain and $R^{\#}$ the set of all nonzero nonunits of $R.\ $For every elements $a,b\in R^{\#},$ we define $a\sim b$ if and only if $aR=bR,$ that is, $a$ and $b$ are associated elements. Suppose that $EC(R^{\#})$ is the set of all equivalence classes of $R^{\#}\ $according to $\sim$.$\ $Let $U_{a}=\{[b]\in EC(R^{\#}):b\ $divides $a\}$ for every $a\in R^{\#}.$ Then we prove that the family $\{U_{a}\}_{a\in R^{\#}}$ becomes a basis for a topology on $EC(R^{\#}).\ $This topology is called divisor topology of $R\ $and denoted by $D(R).\ $We investigate the connections between the algebraic properties of $R\ $and the topological properties of$\ D(R)$. In particular, we investigate the seperation axioms on $D(R)$, first and second countability axioms, connectivity and compactness on $D(R)$. We prove that for atomic domains $R,\ $the divisor topology $D(R)\ $is a Baire space. Also, we characterize valution domains $R$ in terms of nested property of $D(R).$ In the last section, we introduce a new topological proof of the infinitude of prime elements in a UFD and integers by using the topology $D(R)$., Comment: Comments welcome

In this paper, we associate a new topology to a nonzero unital module $M$ over a commutative $R$, which is called Golomb topology of the $R$-module $M$. Let $M\ $be an\ $R$-module and $B_{M}$ be the family of coprime cosets $\{m+N\}$ where $m\in M$ and $N\ $is a nonzero submodule of $M\ $such that $N+Rm=M$. We prove that if $M\ $is a meet irreducible multiplication module or $M\ $is a meet irreducible finitely generated module in which every maximal submodule is strongly irreducible, then $B_{M}\ $is the basis for a topology on $M\ $which is denoted by $\widetilde{G(M)}.$ In particular, the subspace topology on $M-\{0\}$ is called the Golomb topology of the $R$-module $M\ $and denoted by $G(M)$. We investigate the relations between topological properties of $G(M)\ $and algebraic properties of $M.\ $In particular, we characterize some important classes of modules such as simple modules, Jacobson semisimple modules in terms of Golomb topology., Comment: Comments welcome!

This study outlines a detailed investigation using CCD {\it UBV} and {\it Gaia} DR3 data sets of the two open clusters Ruprecht 1 (Rup-1) and Ruprecht 171 (Rup-171). Fundamental astrophysical parameters such as color excesses, photometric metallicities, ages, and isochrone distances were based on {\it UBV}-data analyses, whereas membership probability calculations, structural and astrophysical parameters, as well as the kinematic analyses were based on {\it Gaia} DR3-data. We identified 74 and 596 stars as the most probable cluster members with membership probabilities over 50\% for Rup-1 and Rup-171, respectively. The color excesses $E(B-V)$ were obtained as $0.166\pm0.022$ and $0.301\pm0.027$ mag for Rup-1 and Rup-171, respectively. Photometric metallicity analyses were performed by considering F-G type main-sequence member stars and found to be [Fe/H]=$-0.09\pm 0.16$ and [Fe/H]=$-0.20\pm 0.20$ dex for Rup-1 and Rup-171, respectively. Ages and distances were based on both {\it UBV} and {\it Gaia}-data analyses; according to isochrone-fitting these values were estimated to be $t=580\pm60$ Myr, $d=1469\pm57$ pc for Rup-1 and $t=2700\pm200$ Myr, $d=1509\pm69$ pc for Rup-171. The present-day mass function slope of Rup-1 was estimated as $1.26\pm0.32$ and Rup-171 as $1.53\pm1.49$. Galactic orbit integration analyses showed that both of the clusters might be formed outside the solar circle., Comment: 14 figures and 4 tables, article accepted for publication in Astronomische Nachrichten

This study explores the use of large language models (LLMs) to predict emotion intensity in Polish political texts, a resource-poor language context. The research compares the performance of several LLMs against a supervised model trained on an annotated corpus of 10,000 social media texts, evaluated for the intensity of emotions by expert judges. The findings indicate that while the supervised model generally outperforms LLMs, offering higher accuracy and lower variance, LLMs present a viable alternative, especially given the high costs associated with data annotation. The study highlights the potential of LLMs in low-resource language settings and underscores the need for further research on emotion intensity prediction and its application across different languages and continuous features. The implications suggest a nuanced decision-making process to choose the right approach to emotion prediction for researchers and practitioners based on resource availability and the specific requirements of their tasks., Comment: The Appendix is located at the very bottom of the manuscript

In this study, we attempt to model intuition and incorporate this formalism to improve the performance of the Convolutional Neural Networks. Despite decades of research, ambiguities persist on principles of intuition. Experimental psychology reveals many types of intuition, which depend on state of the human mind. We focus on visual intuition, useful for completing missing information during visual cognitive tasks. First, we set up a scenario to gradually decrease the amount of visual information in the images of a dataset to examine its impact on CNN accuracy. Then, we represent a model for visual intuition using Gestalt theory. The theory claims that humans derive a set of templates according to their subconscious experiences. When the brain decides that there is missing information in a scene, such as occlusion, it instantaneously completes the information by replacing the missing parts with the most similar ones. Based upon Gestalt theory, we model the visual intuition, in two layers. Details of these layers are provided throughout the paper. We use the MNIST data set to test the suggested intuition model for completing the missing information. Experiments show that the augmented CNN architecture provides higher performances compared to the classic models when using incomplete images., Comment: 7 pages, 5 figures, 1 table, submitted to 2024 IEEE International Conference on Image Processing (ICIP), did not get accepted

Wireless communications advance hand-in-hand with artificial intelligence (AI), indicating an interconnected advancement where each facilitates and benefits from the other. This synergy is particularly evident in the development of the sixth-generation technology standard for mobile networks (6G), envisioned to be AI-native. Generative-AI (GenAI), a novel technology capable of producing various types of outputs, including text, images, and videos, offers significant potential for wireless communications, with its distinctive features. Traditionally, conventional AI techniques have been employed for predictions, classifications, and optimization, while GenAI has more to offer. This article introduces the concept of strategic demand-planning through demand-labeling, demand-shaping, and demand-rescheduling. Accordingly, GenAI is proposed as a powerful tool to facilitate demand-shaping in wireless networks. More specifically, GenAI is used to compress and convert the content of various kind (e.g., from a higher bandwidth mode to a lower one, such as from a video to text), which subsequently enhances performance of wireless networks in various usage scenarios such as cell-switching, user association and load balancing, interference management, and disaster scenarios management. Therefore, GenAI can serve a function in saving energy and spectrum in wireless networks. With recent advancements in AI, including sophisticated algorithms like large-language-models and the development of more powerful hardware built exclusively for AI tasks, such as AI accelerators, the concept of demand-planning, particularly demand-shaping through GenAI, becomes increasingly relevant. Furthermore, recent efforts to make GenAI accessible on devices, such as user terminals, make the implementation of this concept even more straightforward and feasible.

Large language models (LLMs) are commonly trained on datasets consisting of fixed-length token sequences. These datasets are created by randomly concatenating documents of various lengths and then chunking them into sequences of a predetermined target length. However, this method of concatenation can lead to cross-document attention within a sequence, which is neither a desirable learning signal nor computationally efficient. Additionally, training on long sequences becomes computationally prohibitive due to the quadratic cost of attention. In this study, we introduce dataset decomposition, a novel variable sequence length training technique, to tackle these challenges. We decompose a dataset into a union of buckets, each containing sequences of the same size extracted from a unique document. During training, we use variable sequence length and batch size, sampling simultaneously from all buckets with a curriculum. In contrast to the concat-and-chunk baseline, which incurs a fixed attention cost at every step of training, our proposed method incurs a penalty proportional to the actual document lengths at each step, resulting in significant savings in training time. We train an 8k context-length 1B model at the same cost as a 2k context-length model trained with the baseline approach. Experiments on a web-scale corpus demonstrate that our approach significantly enhances performance on standard language evaluations and long-context benchmarks, reaching target accuracy 3x faster compared to the baseline. Our method not only enables efficient pretraining on long sequences but also scales effectively with dataset size. Lastly, we shed light on a critical yet less studied aspect of training large language models: the distribution and curriculum of sequence lengths, which results in a non-negligible difference in performance.

This study aims to introduce the cell load estimation problem of cell switching approaches in cellular networks specially-presented in a high-altitude platform station (HAPS)-assisted network. The problem arises from the fact that the traffic loads of sleeping base stations for the next time slot cannot be perfectly known, but they can rather be estimated, and any estimation error could result in divergence from the optimal decision, which subsequently affects the performance of energy efficiency. The traffic loads of the sleeping base stations for the next time slot are required because the switching decisions are made proactively in the current time slot. Two different Q-learning algorithms are developed; one is full-scale, focusing solely on the performance, while the other one is lightweight and addresses the computational cost. Results confirm that the estimation error is capable of changing cell switching decisions that yields performance divergence compared to no-error scenarios. Moreover, the developed Q-learning algorithms perform well since an insignificant difference (i.e., 0.3%) is observed between them and the optimum algorithm.

It is crucial to deploy temporary non-terrestrial networks (NTN) in disaster situations where terrestrial networks are no longer operable. Deploying uncrewed aerial vehicle base stations (UAV-BSs) can provide a radio access network (RAN); however, the backhaul link may also be damaged and unserviceable in such disaster conditions. In this regard, high-altitude platform stations (HAPS) spark attention as they can be deployed as super macro base stations (SMBS) and data centers. Therefore, in this study, we investigate a three-layer heterogeneous network with different topologies to prolong the lifespan of the temporary network by using UAV-BSs for RAN services and HAPS-SMBS as a backhaul. Furthermore, a two-layer clustering algorithm is proposed to handle the UAV-BS ad-hoc networking effectively.

In this study, we investigate the fundamental astrophysical parameters of the old open cluster NGC 188 through two complementary methods: isochron-fitting and spectral energy distribution (SED) analysis. Using photometric, astrometric, and spectroscopic data from the Gaia Data Release 3, we identify 868 most likely member stars with membership probabilities $P \geq 0.5$. The mean proper-motion components and trigonometric parallaxes of the cluster are derived as ($\mu_{\alpha}\cos \delta$, $\mu_{\delta}$) = (-$2.314 \pm 0.002$, -$1.022 \pm 0.002$) mas yr$^{-1}$ and $\varpi = 0.550 \pm 0.023$, respectively. From this initial selection of high probable member stars, we proceed with the determination of astrophysical parameters using the isochron-fitting method. Simultaneously estimating the colour excess, distance, and age of the cluster, we employee PARSEC isochrones to observational data on Gaia based colour-magnitude diagrams. These findings were obtained as $E(G_{BP}-G_{RP})=0.066\pm 0.012$ mag, $d=1806 \pm21$ pc, and $t=7.65 \pm 1.00$ Gyr, respectively. Additionally, we identify and detected 19 previously confirmed blue straggler stars within NGC 188. Subsequently, we performed SED analyses for 412 out of the 868 cluster members. We obtained colour excess, distance and age of the cluster as $E(B-V)=0.034\pm 0.030$ mag, $d=1854\pm 148$ pc, and $t=7.78\pm 0.23$ Gyr, respectively. The analysis of member stars was revealed patterns of extinction in the $V$-band, with higher values of A(V) observed in the lower right quadrant of the cluster. By comparing our results of SED analysis with models of stellar evolution, particularly in terms of temperature and surface gravity, we confirm agreement with theoretical predictions. This comprehensive investigation sheds light on the astrophysical properties of NGC 188, contributing to our understanding of stellar evolution within open clusters., Comment: 25 pages, 14 figures and 5 tables, accepted for publication in Physics and Astronomy Reports

In this article, we introduce the notion of regular fusible modules. Let $R$ be a ring with an identity and $M$ an $R$-module. An element $0\neq m\in M$ is said to be regular fusible if there exists $r\in R$, a non zero-divisor of $M$, such that $mr$ can be written as the sum of a torsion element and a torsion free element in $M$. $M$ is called regular fusible if every nonzero element of $M$ is regular fusible. We characterize regular fusible modules in terms of fusible modules. In addition, we show that a regular fusible module over a right duo ring is reduced and nonsingular. Moreover, we study the regular fusible property under Cartesian product, trivial extension ring, and module of a fractions. Also, we characterize division rings in terms of fusible modules.

This study investigates the integration of a high altitude platform station (HAPS), a non-terrestrial network (NTN) node, into the cell-switching paradigm for energy saving. By doing so, the sustainability and ubiquitous connectivity targets can be achieved. Besides, a delay-aware approach is also adopted, where the delay profiles of users are respected in such a way that we attempt to meet the latency requirements of users with a best-effort strategy. To this end, a novel, simple, and lightweight Q-learning algorithm is designed to address the cell-switching optimization problem. During the simulation campaigns, different interference scenarios and delay situations between base stations are examined in terms of energy consumption and quality-of-service (QoS), and the results confirm the efficacy of the proposed Q-learning algorithm.

We investigate feature selection problem for generic machine learning (ML) models. We introduce a novel framework that selects features considering the predictions of the model. Our framework innovates by using a novel feature masking approach to eliminate the features during the selection process, instead of completely removing them from the dataset. This allows us to use the same ML model during feature selection, unlike other feature selection methods where we need to train the ML model again as the dataset has different dimensions on each iteration. We obtain the mask operator using the predictions of the ML model, which offers a comprehensive view on the subsets of the features essential for the predictive performance of the model. A variety of approaches exist in the feature selection literature. However, no study has introduced a training-free framework for a generic ML model to select features while considering the importance of the feature subsets as a whole, instead of focusing on the individual features. We demonstrate significant performance improvements on the real-life datasets under different settings using LightGBM and Multi-Layer Perceptron as our ML models. Additionally, we openly share the implementation code for our methods to encourage the research and the contributions in this area.

We study the problem of feature selection in general machine learning (ML) context, which is one of the most critical subjects in the field. Although, there exist many feature selection methods, however, these methods face challenges such as scalability, managing high-dimensional data, dealing with correlated features, adapting to variable feature importance, and integrating domain knowledge. To this end, we introduce the "Adaptive Feature Selection with Binary Masking" (AFS-BM) which remedies these problems. AFS-BM achieves this by joint optimization for simultaneous feature selection and model training. In particular, we do the joint optimization and binary masking to continuously adapt the set of features and model parameters during the training process. This approach leads to significant improvements in model accuracy and a reduction in computational requirements. We provide an extensive set of experiments where we compare AFS-BM with the established feature selection methods using well-known datasets from real-life competitions. Our results show that AFS-BM makes significant improvement in terms of accuracy and requires significantly less computational complexity. This is due to AFS-BM's ability to dynamically adjust to the changing importance of features during the training process, which an important contribution to the field. We openly share our code for the replicability of our results and to facilitate further research.

In this study, we aim to introduce the concept of classical 1-absorbing prime submodules of a nonzero unital module $M$ over a commutative ring $A$ with unity. A proper submodule $P$ of $M$ is said to be a classical 1-absorbing prime submodule, if for each $m\in M$ and nonunits $a,b,c\in A,$ $abcm\in P$ implies that $abm\in P$ or $cm\in P$. We give many examples and properties of classical 1-absorbing prime submodules. Also, we investiage the classical 1-absorbing prime submodules of tensor product $F\otimes M$ of a (faithfully) flat $A$-module $F$ and any $A$-module $M$. Furthermore, we determine classical prime, classical 1-absorbing prime and classical 2-absorbing submodules of amalgamated duplication $M\bowtie I$ of an $A$-module $M$ along an ideal $I$. Also, we characterize local rings $(A,\mathfrak{m})$ with $\mathfrak{m}^{2}=0$ in terms of classical 1-absorbing prime submodules., Comment: 17 pages. arXiv admin note: text overlap with arXiv:2403.19659

In this paper, we study weakly classical 1-absorbing prime submodules of a nonzero unital module $M$ over a commutative ring $R$ having a nonzero identity. A proper submodule $N$ of $M$ is said to be a weakly classical 1-absorbing prime submodule, if for each $m\in M$ and nonunits $a,b,c\in R,$ $0\neq abcm\in N$ implies that $abm\in N$ or $cm\in N$. We give various examples and properties of weakly classical 1-absorbing prime submodules. Also, we investiage the weakly classical 1-absorbing prime submodules of tensor product $F\otimes M$ of a (faithfully) flat $R$-module $F$ and any $R$-module $M.$ Also, we prove that if every proper submodule of an $R$-module $M$ is weakly classical 1-absorbing prime, then $Jac(R)^{3}M=0$. In terms of this result, we characterize modules over local rings in which every proper submodule is weakly classical 1-absorbing prime., Comment: 16 pages